Most home insurance does not cover your items while they are being moved by a moving company. They may be covered while being packed, in your house, but not while outside or in transit. A reputable moving company will have its own insurance policy, although it may not be easy to collect. If you are curious whether your possessions are covered, you should ask your agent. Try to get the answer in writing, if you can.
If you do the move yourself, your stuff may be covered, since it is always in your possession. You should tell your agent whether you are doing the move yourself or if you are going to use a service.